Energy and Laplacian on the Sierpiński Gasket

Some Spectral Properties of Pseudo-differential Operators on the Sierpiński Gasket

We prove versions of the strong Szëgo limit theorem for certain classes of pseudodifferential operators defined on the Sierpiński gasket. Our results used in a fundamental way the existence of localized eigenfunctions for the Laplacian on this fractal.

Szegö Limit Theorems on the Sierpiński Gasket

We use the existence of localized eigenfunctions of the Laplacian on the Sierpiński gasket (SG) to formulate and prove analogues of the strong Szegö limit theorem in this fractal setting. Furthermore, we recast some of our results in terms of equally distributed sequences.

Multiple solutions for a class of nonlinear elliptic equations on the Sierpiński gasket

The anisotropic quantum antiferromagnet on the Sierpiński gasket: Ground state and thermodynamics

We investigate an antiferromagnetic s=1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpiński gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to a the Sierpiński gasket with N=42. Using this and other methods we calculate ground state energies, spin gap, spin–spin correlation...

Coloring Sierpiński graphs and Sierpiński gasket graphs

Sierpiński graphs S(n, 3) are the graphs of the Tower of Hanoi with n disks, while Sierpiński gasket graphs Sn are the graphs naturally defined by the finite number of iterations that lead to the Sierpiński gasket. An explicit labeling of the vertices of Sn is introduced. It is proved that Sn is uniquely 3-colorable, that S(n, 3) is uniquely 3-edgecolorable, and that χ′(Sn) = 4, thus answering ...